Mounting devices are used to attach objects to a tire, and particularly to the innerliner of a tire. One application is to attach a radio frequency identification tag or chip (RFID) to the innerliner of a tire. Another such application is to secure a pressure and/or temperature-sensing device to the innerliner of the tire. Various fasteners are used to connect the object to the mounting device, including hook and loop fasteners, threaded connectors, clamps, pins, and snap-fit structures.